A308267 Numbers k such that k divides A048678(k).

1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 83, 112, 124, 127, 128, 166, 224, 248, 254, 256, 332, 397, 448, 496, 508, 511, 512, 664, 794, 891, 896, 992, 1016, 1022, 1024, 1163, 1328, 1588, 1782, 1792, 1984, 2032, 2044, 2047, 2048, 2326, 2656, 3176, 3441, 3564, 3584, 3968

Offset

1,2

Comments

Apparently includes all powers of 2.

All numbers 2^(2k+1)-1 are in this sequence, and if n is in this sequence then so is 2n. - Charlie Neder, May 17 2019

Links

Table of n, a(n) for n=1..55.

Example

The first few terms of A048678 are 1,2,5,4,9,10,21,8. 2 is a multiple of 2, 5 isn't a multiple of 3, 4 is a multiple of 4, 9 isn't a multiple of 5, 10 isn't a multiple of 6, 21 is a multiple of 7, etc.

Mathematica

Select[Range[4000], Divisible[FromDigits[Flatten[IntegerDigits[#, 2] /. {1 -> {0, 1}}], 2], #] &] (* Amiram Eldar, Jul 08 2019 after Robert G. Wilson v at A048678 *)

Prog

(Haskell) bintodec :: [Integer] -> Integerbintodec = sum . zipWith (*) (iterate (*2) 1) . reverse
decomp :: (Integer, [Integer]) -> (Integer, [Integer])decomp (x, ys) = if even x then (x `div` 2, 0:ys) else (x - 1, 1:ys)
zeck :: Integer -> Integerzeck n = bintodec (1 : snd (last . takeWhile (\(x, _) -> x > 0) $ iterate decomp (n, [])))
output :: [Integer]output = filter (\x -> 0 == zeck x `mod` x) [1..100]
main :: IO ()main = print output

Crossrefs

Cf. A048678, A083420 (subsequence).

Sequence in context: A324588 A201364 A225318 * A177805 A003591 A029746

Adjacent sequences: A308264 A308265 A308266 * A308268 A308269 A308270

Keyword

nonn,base

Author

Dan Dart, May 17 2019

Status

approved